Abstract
In this chapter, we investigate the topological structure of solution sets for stochastic evolution inclusions in Hilbert spaces in cases that semigroup is compact and noncompact, respectively. It is shown that the solution set is nonempty, compact and \(R_\delta \) -set which means that the solution set may not be a singleton but, from the point of view of algebraic topology, it is equivalent to a point, in the sense that it has the same homology group as one-point space. As applications of the obtained results, an example is given.
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Zhou, Y., Wang, RN., Peng, L. (2017). Stochastic Evolution Inclusions. In: Topological Structure of the Solution Set for Evolution Inclusions. Developments in Mathematics, vol 51. Springer, Singapore. https://doi.org/10.1007/978-981-10-6656-6_8
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DOI: https://doi.org/10.1007/978-981-10-6656-6_8
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6655-9
Online ISBN: 978-981-10-6656-6
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